The 12th-seeded Frenchman, runner-up to Novak Djokovic last year, will next face Fernando Verdasco of Spain. Verdasco needs to reach the semifinals to stand a chance of playing in the ATP Finals in London later this month.
Former champion Tomas Berdych of the Czech Republic, seeded fifth, also remained in contention when he routed Florent Serra of France 6-3, 6-1 in only 47 minutes. Berdych won the Paris Masters in 2005.
Three berths for the London event from Nov. 21-28 are up for grabs in Paris with five players still competing for a spot at the year-end tournament. Andy Roddick, David Ferrer and Jurgen Melzer are also vying for a place.
Both players were playing patchy tennis and swapped breaks at the start of the second set, before Monfils -- who won his third career title at the Open Sud de France last month -- broke Becker in the seventh game and held for a 5-3 lead.
"I honestly don't know how I won the first set, [trailing] 4-0 and 5-1," Monfils said. "But the fans really got behind me."
Monfils, who was limping at times, put ice on his knee after the match.
"It was tough because I was also really tired and because I didn't start very well," he said.
Serving for the match, Monfils fell behind 0-40 but regained his composure and sealed the win with a cross-court backhand.
Earlier, Mikhail Youzhny retired from his second round match with a back injury, relinquishing any hope of qualifying for the ATP Finals.
The ninth-seeded Russian retired while trailing against Ernests Gulbis of Latvia 6-4, 3-0. Youzhny was in 10th place in the ATP Finals race and needed to reach the final in Paris to have a chance to qualify.
Gulbis will next play either Roddick of Jarkko Nieminen of Finland.
Verdasco kept an outside chance of qualifying after rallying from a set and a break down to beat Arnaud Clement 3-6, 6-3, 6-0.
The sixth-seeded Spaniard, who claimed only his second win since reaching the U.S. Open quarterfinals, made the most of Clement's sudden drop of form to win the last 10 games of the match.
"In the third set I saw him a little bit tired," the left-handed Verdasco said. "He started making double faults at the end of the second set and the beginning of the third set, so this helped me to take advantage and break him and take more confidence also in my game. Finally I finished playing good."
"Tomorrow is going to be one of those matches you really want to play and really want to win," Nalbandian said. "He is a very complete player and it's difficult to play offensively against him."
Simon rallied from 4-2 down in the second set and next plays fourth-seeded Robin Soderling.
"I fought back. I had the feeling he was playing a lot better than I was," Simon said. "At 4-3 [ahead] he played a bad game. He made two double faults and two unforced errors."
The center court in Paris is faster this year, which should suit top-seeded Roger Federer in his bid to win the tournament for the first time. The 16-time Grand Slam champion has never advanced past the quarterfinals at the Paris Masters.
"I think it's nice that some tournaments have made the courts faster again," said Federer, who will start against Richard Gasquet on Wednesday. "I'm not saying it should be the trend for all the tournaments, but indoor is supposed to be faster. We only have one indoor Masters 1000, so I think it should be the fastest one, which is the case."